Bitte verwenden Sie diesen Link, um diese Publikation zu zitieren, oder auf sie als Internetquelle zu verweisen: https://hdl.handle.net/10419/324260 
Erscheinungsjahr: 
2020
Schriftenreihe/Nr.: 
Center for Mathematical Economics Working Papers No. 716
Verlag: 
Bielefeld University, Center for Mathematical Economics (IMW), Bielefeld
Zusammenfassung: 
We consider convex monotone semigroups on a Banach lattice, which is assumed to be a Riesz subspace of a σ -Dedekind complete Banach lattice with an additional assumption on the dual space. As typical examples, we consider the space of bounded uniformly continuous functions and the space of continuous functions vanishing at infinity. We show that the domain of the classical generator for convex monotone C0-semigroups, which is defined in terms of the time derivative at 0 w.r.t. the supremum norm, is typically not invariant. We thus propose alternative forms of generators and domains, for which we prove the invariance under the semigroup. As a consequence, we obtain the uniqueness of the semigroup in terms of an extended version of the generator. The results are discussed in several examples related to fully nonlinear partial differential equations, such as uncertain shift semigroups and semigroups related to G-heat equations (fully nonlinear versions of the heat equation).
Schlagwörter: 
Convex semigroup
nonlinear Cauchy problem
fully nonlinear PDE
uniqueness
Hamilton-Jacobi-Bellman equation
Persistent Identifier der Erstveröffentlichung: 
Creative-Commons-Lizenz: 
cc-by Logo
Dokumentart: 
Working Paper

Datei(en):
Datei
Größe
440.51 kB





Publikationen in EconStor sind urheberrechtlich geschützt.